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Proof step 26 from proof bits2bytes-app (previous step)

# bits0 % 8 = 0, 8 < # bits + # bits0, 8 ≤ # bits0, ∀ bits1, bits2. # bits2 + # bits1 < # bits + # bits0 → # bits1 % 8 = 0 → bits2 = [] ∨ bits1 = [] ∨ bits2bytes(bits2 + bits1) = bits2bytes(bits2) + bits2bytes(bits1) ⊦ bits2bytes(firstn(# bits + (# bits0 - 8), bits + bits0)) + i2b(bits2int(lastn(8, bits0))) ' = bits2bytes(bits) + bits2bytes(bits0), bits0 = [], bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ 8 < # bits → bits2bytes(bits) = bits2bytes(firstn(# bits - 8, bits)) + i2b(bits2int(lastn(8, bits)))
Proof step 28:
¬ 8 < # bits0, # bits0 % 8 = 0, 8 < # bits + # bits0, 8 ≤ # bits0, ∀ bits1, bits2. # bits2 + # bits1 < # bits + # bits0 → # bits1 % 8 = 0 → bits2 = [] ∨ bits1 = [] ∨ bits2bytes(bits2 + bits1) = bits2bytes(bits2) + bits2bytes(bits1) ⊦ bits2bytes(firstn(# bits + (# bits0 - 8), bits + bits0)) + i2b(bits2int(lastn(8, bits0))) ' = bits2bytes(bits) + bits2bytes(bits0), bits0 = [], bits = []
Proof step 31:
8 < # bits0, # bits0 % 8 = 0, 8 < # bits + # bits0, 8 ≤ # bits0, ∀ bits1, bits2. # bits2 + # bits1 < # bits + # bits0 → # bits1 % 8 = 0 → bits2 = [] ∨ bits1 = [] ∨ bits2bytes(bits2 + bits1) = bits2bytes(bits2) + bits2bytes(bits1) ⊦ bits2bytes(firstn(# bits + (# bits0 - 8), bits + bits0)) + i2b(bits2int(lastn(8, bits0))) ' = bits2bytes(bits) + (bits2bytes(firstn(# bits0 - 8, bits0)) + i2b(bits2int(lastn(8, bits0)))), bits0 = [], bits = []

Rule argument

name: bits2bytes-rec rotate: F subst: [bits] → [bits0]

Additional information

Used terms: bits0